CORPORATE FINANCE FORMULAS 2024 #16
Present Value = - correct answer Cash Flow/ (1+r)ⁿ = Discount Factor × Cash Flow
Where discount factor= 1/1+r
Rate of return r - correct answer Profit/Investment
(aka discount rate, hurdle rate, opportunity cost of capital)
Return foregone by investors by investing in the project rather than other investments of
equivalent risk (e.g., financial markets)
Net Present Value = - correct answer Present Value - Investment
C₀ + C₁/(1+r) = C₀ + 1/1+r × C₁,
Where C₀ is investment and so negative
Net present value NPV rule for capital investment - correct answer accept investments
that have positive net present values
Rate of return IRR rule of capital investment - correct answer accept investments that
offer rates of return in excess of their opportunity cost of capital. IRR exceeds the
discount rate whenever the NPV is positive.
DCF formula - correct answer PV equals a sum of present values of future cash flows
PV= C₁/(1+r) + C₂/(1+r)² + C₃/(1+r)³.... PV= ∑C/(1+r)ⁿ
PV of perpetuity - correct answer PV=C/r
Not to be confused with PV of a single payment PV=C/(1+r)
Discount factor - correct answer 1/(1+r)ⁿ, where n refers to the number of years from
now
Rate of return on a perpetuity - correct answer Payment/Present Value
R=C/PV
PV of ordinary annuity for t years - correct answer PV (perpetuity A) - PV (perpetuity B)
= C/r - C/(r(1+r)ⁿ)
The difference in the pvs of a perpetuity now (1st payment at the end of this year) and
PV of another perpetuity with first payments at the end of t years
PV of annuity due (i.e., payments at the start of year) = - correct answer PV (annuity
due) = PV (ordinary annuity) × (1+r)
PV of growing perpetuity (stream of cash flow grows at constant rate g) - correct answer
PV=C₁/r-g, where C₁ is a cash flow received a year from now. R must be greater than g.
PV of growing annuity - correct answer = (C/r-g) × (1-(1+g)ⁿ/(1+r)ⁿ)
, Future Value = - correct answer C₀ × (1+r)
Value of business - correct answer is the present value of the free cash flows generated
by the business
Calculating NPV - correct answer 1. Forecast incremental cash flows generated by the
project
2. Determine the appropriate discount rate = opportunity cost of capital
3. Calculate the sum of pvs of cash inflows, minus initial investment
Payback Period - correct answer time taken by the project to return the initial investment
in the project (rather unreliable measure)
Internal Rate of Return - correct answer discount rate at which NPV equals zero
Calculating after-tax FCF - correct answer 1. Get pre-tax CF
A: EBIT (aka operating income = sales - cost - depreciation) + depreciation - CAPEX -
increase in NWC.
B: Sales - Cost - CAPEX - increase in NWC
2. Pre-tax CF - Tax (tax rate × sales - cost - tax depreciation)
Depreciation 20% declining balance - correct answer each year the allowance shrinks
by 20%
Real terms - correct answer inflation-adjusted
Converting real discount rate to nominal - correct answer R = r + i , where r is real
discount rate and i is inflation.
The exact formula is:
1 + R = (1 + r ) (1 + i )
Working capital is: - correct answer inventories
Work-in-progress
Accounts receivable less payables.
Expected cash flows - correct answer average value of the cash flows across all
different possible outcomes, weighted by the chances of the
Outcomes
Safest investment - correct answer Treasury Bills: no risk of default, short term
maturity=stable prices. Only uncertainty is real rate of return (due to inflation)
Prices of long-term gov bonds rise when... Fall when - correct answer interest rates
fall... Interest rates rise
Present Value = - correct answer Cash Flow/ (1+r)ⁿ = Discount Factor × Cash Flow
Where discount factor= 1/1+r
Rate of return r - correct answer Profit/Investment
(aka discount rate, hurdle rate, opportunity cost of capital)
Return foregone by investors by investing in the project rather than other investments of
equivalent risk (e.g., financial markets)
Net Present Value = - correct answer Present Value - Investment
C₀ + C₁/(1+r) = C₀ + 1/1+r × C₁,
Where C₀ is investment and so negative
Net present value NPV rule for capital investment - correct answer accept investments
that have positive net present values
Rate of return IRR rule of capital investment - correct answer accept investments that
offer rates of return in excess of their opportunity cost of capital. IRR exceeds the
discount rate whenever the NPV is positive.
DCF formula - correct answer PV equals a sum of present values of future cash flows
PV= C₁/(1+r) + C₂/(1+r)² + C₃/(1+r)³.... PV= ∑C/(1+r)ⁿ
PV of perpetuity - correct answer PV=C/r
Not to be confused with PV of a single payment PV=C/(1+r)
Discount factor - correct answer 1/(1+r)ⁿ, where n refers to the number of years from
now
Rate of return on a perpetuity - correct answer Payment/Present Value
R=C/PV
PV of ordinary annuity for t years - correct answer PV (perpetuity A) - PV (perpetuity B)
= C/r - C/(r(1+r)ⁿ)
The difference in the pvs of a perpetuity now (1st payment at the end of this year) and
PV of another perpetuity with first payments at the end of t years
PV of annuity due (i.e., payments at the start of year) = - correct answer PV (annuity
due) = PV (ordinary annuity) × (1+r)
PV of growing perpetuity (stream of cash flow grows at constant rate g) - correct answer
PV=C₁/r-g, where C₁ is a cash flow received a year from now. R must be greater than g.
PV of growing annuity - correct answer = (C/r-g) × (1-(1+g)ⁿ/(1+r)ⁿ)
, Future Value = - correct answer C₀ × (1+r)
Value of business - correct answer is the present value of the free cash flows generated
by the business
Calculating NPV - correct answer 1. Forecast incremental cash flows generated by the
project
2. Determine the appropriate discount rate = opportunity cost of capital
3. Calculate the sum of pvs of cash inflows, minus initial investment
Payback Period - correct answer time taken by the project to return the initial investment
in the project (rather unreliable measure)
Internal Rate of Return - correct answer discount rate at which NPV equals zero
Calculating after-tax FCF - correct answer 1. Get pre-tax CF
A: EBIT (aka operating income = sales - cost - depreciation) + depreciation - CAPEX -
increase in NWC.
B: Sales - Cost - CAPEX - increase in NWC
2. Pre-tax CF - Tax (tax rate × sales - cost - tax depreciation)
Depreciation 20% declining balance - correct answer each year the allowance shrinks
by 20%
Real terms - correct answer inflation-adjusted
Converting real discount rate to nominal - correct answer R = r + i , where r is real
discount rate and i is inflation.
The exact formula is:
1 + R = (1 + r ) (1 + i )
Working capital is: - correct answer inventories
Work-in-progress
Accounts receivable less payables.
Expected cash flows - correct answer average value of the cash flows across all
different possible outcomes, weighted by the chances of the
Outcomes
Safest investment - correct answer Treasury Bills: no risk of default, short term
maturity=stable prices. Only uncertainty is real rate of return (due to inflation)
Prices of long-term gov bonds rise when... Fall when - correct answer interest rates
fall... Interest rates rise
